One time when I was a kid I was playing with my older sister's graphing calculator. I had accidentally pressed the base button and now was in hex mode. I did some benign calculation like 10+10 and got 14. I believed it!

I went to school the next day and told my teacher that the calculator says that 10+10 is 14, so why does she say it's 20?

So she showed me on her calculator. She pressed the hex button and explained why it was 14.

I think a major problem with people's usage of LLMs is that they stop at 10+10=14. They don't question it or ask someone (even the LLM) to explain the answer.

> Catching an LLM hallucinating often takes a basic understanding of what the answer should look like before asking the question.

We had the same problem in the early days of calculators. Using a slide rule, you had to track the order of magnitude in your head; this habit let you spot a large class of errors (things that weren't even close to correct).

When calculators came on the scene, people who never used a slide rule would confidently accept answers that were wildly incorrect (example: a mole of ideal gas at STP is 22.4 liters. If you typo it as 2204, you get an answer that's off by roughly two orders of magnitude, say 0.0454 when it should be 4.46. Easy to spot if you know roughly what the answer should look like, but easy to miss if you don't).